Rinse the sushi rice under cold water until the water runs clear. Cook the rice with water in a rice cooker or pot until tender.

In a small saucepan, heat rice vinegar, sugar, and salt until dissolved. Gently fold this mixture into the cooked rice and let it cool to room temperature.

Place a bamboo sushi mat on a clean surface and cover it with plastic wrap. Lay a sheet of nori on top, shiny side down.

Wet your hands and spread a thin layer of rice evenly over the nori, leaving a 1-inch border at the top.

Arrange slices of fish, avocado, and cucumber in a line along the bottom edge of the rice-covered nori.

Roll the sushi tightly using the bamboo mat, applying gentle pressure. Slice into bite-sized pieces with a sharp, wet knife.

Serve with soy sauce, wasabi, and pickled ginger on the side.